A simulation-based estimation method for bias reduction

ABSTRACT

Models are often built to evaluate system performance measures or to make quantitative decisions. These models sometimes involve unknown input parameters that need to be estimated statistically using data. In these situations, a statistical method is typically used to estimate these input parameters and the estimates are then plugged into the models to evaluate system output performances. The output performance estimators obtained from this approach usually have large bias when the model is nonlinear and the sample size of the data is finite. A simulation-based estimation method to reduce the bias of performance estimators for models that have a closed-form expression already exists in the literature. In this article, we extend that method to more general situations where the models have no closed-form expression and can only be evaluated through simulation. A stochastic root-finding problem is formulated to obtain the simulation-based estimators and several algorithms are designed. Furthermore, we give a thorough asymptotic analysis of the properties of the simulation-based estimators, including the consistency, the order of the bias, the asymptotic variance, and so on. Our numerical experiments show that the experimental results are consistent with the theoretical analysis.

KEYWORDS:

• Simulation-based estimation
• bias reduction
• stochastic root-finding
• asymptotic analysis

Acknowledgements

The authors thank the Associate Editor and two anonymous referees for their insightful and helpful comments that have greatly improved this work. A preliminary version of this article (Fang and Hong, 2013) was published in the Proceedings of the 2013 Winter Simulation Conference.

Funding

This research was supported in part by the Hong Kong Research Grants Council (GRF 613213, GRF 11270116, and T32-102/14N).

Notes

1 When analyzing the bias, we need the uniform integrability of the remainder. We follow the convention of some statistical literature such as Gouriéroux and Monfort (1995) and choose to ignore this issue for simplicity.

Additional information

Notes on contributors

Jin Fang

Jin Fang is currently a Research Associate in the Department of Industrial Engineering and Logistics Management at the Hong Kong University of Science and Technology (HKUST). She received her B.Eng. from the University of Science and Technology of China (2010) and her Ph.D. in Operations Research from the HKUST (2015). Her research interests include stochastic modeling, simulation-based optimization, numerical methods, and algorithms with their applications in operations management.

L. Jeff Hong

L. Jeff Hong received his Ph.D. in Industrial Engineering and Management Science from Northwestern University and his B.S. in Automotive Engineering from Tsinghua University. He is currently Chair Professor of Management Sciences in College of Business at City University of Hong Kong. His research interests include stochastic optimization and simulation, financial engineering and risk management, and business analytics.